{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "5376b303-f96f-4db4-822f-bcc70f518082",
   "metadata": {},
   "source": [
    "\n",
    "---\n",
    "\n",
    "### 🎯 一、线性回归的基本公式\n",
    "\n",
    "模型的预测公式为：\n",
    "\n",
    "$$\n",
    "\\hat{y} = wx + b\n",
    "$$\n",
    "\n",
    "* $x$：输入特征\n",
    "* $w$：权重\n",
    "* $b$：偏置\n",
    "* $\\hat{y}$：模型预测值\n",
    "* $y$：真实值\n",
    "\n",
    "---\n",
    "\n",
    "### 🎯 二、损失函数：均方误差（MSE）\n",
    "\n",
    "$$\n",
    "J(w, b) = \\frac{1}{n} \\sum_{i=1}^{n} (wx_i + b - y_i)^2\n",
    "$$\n",
    "\n",
    "目标是最小化这个损失函数，因此我们要对它求偏导数。\n",
    "\n",
    "---\n",
    "\n",
    "### 🧮 三、对权重 w 求导（梯度）\n",
    "\n",
    "我们要计算：\n",
    "\n",
    "$$\n",
    "\\frac{\\partial J}{\\partial w} = \\frac{1}{n} \\sum_{i=1}^{n} 2(wx_i + b - y_i) \\cdot x_i\n",
    "$$\n",
    "\n",
    "把常数 2 提前，就得到：\n",
    "\n",
    "$$\n",
    "\\frac{\\partial J}{\\partial w} = \\frac{2}{n} \\sum_{i=1}^{n} (wx_i + b - y_i) \\cdot x_i\n",
    "$$\n",
    "\n",
    "也就是你代码里的这句：\n",
    "\n",
    "```python\n",
    "dw = (2 / len(x)) * np.dot(error, x)\n",
    "```\n",
    "\n",
    "其中：\n",
    "\n",
    "* `error = y_pred - y`\n",
    "* `np.dot(error, x)` 相当于求和 $\\sum_i (wx_i + b - y_i) \\cdot x_i$\n",
    "\n",
    "---\n",
    "\n",
    "### 🧮 四、对偏置 b 求导\n",
    "\n",
    "对 b 求导更简单：\n",
    "\n",
    "$$\n",
    "\\frac{\\partial J}{\\partial b} = \\frac{1}{n} \\sum_{i=1}^{n} 2(wx_i + b - y_i)\n",
    "$$\n",
    "\n",
    "$$\n",
    "= \\frac{2}{n} \\sum_{i=1}^{n} (wx_i + b - y_i)\n",
    "$$\n",
    "\n",
    "也就是你代码中的：\n",
    "\n",
    "```python\n",
    "db = (2 / len(x)) * np.sum(error)\n",
    "```\n",
    "\n",
    "---\n",
    "\n",
    "### ✅ 五、结论\n",
    "\n",
    "* 这两个导数（梯度）告诉我们当前参数 w 和 b 的方向偏离了最优解多少；\n",
    "* 用它们可以进行**梯度下降**，逐步优化模型；\n",
    "* 这种推导方式是机器学习中最基础的优化过程。\n",
    "\n",
    "---\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "fe41b43c-e6fe-40c1-9dec-cb0ae08fdb9d",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "训练完成：w = 0.6177, b = 2.1361\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 一元线性回归\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "plt.rc(\"font\", family='Microsoft YaHei')\n",
    "# 构造数据\n",
    "x = np.array([1, 2, 3, 4, 5])\n",
    "y = np.array([2, 4, 5, 4, 5])\n",
    "\n",
    "# 初始化参数\n",
    "w = 0.0\n",
    "b = 0.0\n",
    "lr = 0.01\n",
    "epochs = 1000\n",
    "\n",
    "# 梯度下降训练\n",
    "for i in range(epochs):\n",
    "    y_pred = w * x + b\n",
    "    error = y_pred - y\n",
    "\n",
    "    dw = (2 / len(x)) * np.dot(error, x)\n",
    "    db = (2 / len(x)) * np.sum(error)\n",
    "\n",
    "    w -= lr * dw\n",
    "    b -= lr * db\n",
    "\n",
    "# 打印最终模型参数\n",
    "print(f\"训练完成：w = {w:.4f}, b = {b:.4f}\")\n",
    "\n",
    "# 可视化结果\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.scatter(x, y, color='blue', label='原始数据')\n",
    "plt.plot(x, w * x + b, color='red', label='拟合直线')\n",
    "plt.title('线性回归拟合图')\n",
    "plt.xlabel('x')\n",
    "plt.ylabel('y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "794e4777-e2bf-4f3c-ae7c-a000309d92c4",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "梯度下降迭代0: 损失 J(θ) = 13.1652\n",
      "梯度下降迭代100: 损失 J(θ) = 0.2282\n",
      "梯度下降迭代200: 损失 J(θ) = 0.1395\n",
      "梯度下降迭代300: 损失 J(θ) = 0.1179\n",
      "梯度下降迭代400: 损失 J(θ) = 0.1116\n",
      "梯度下降迭代500: 损失 J(θ) = 0.1094\n",
      "梯度下降迭代600: 损失 J(θ) = 0.1086\n",
      "梯度下降迭代700: 损失 J(θ) = 0.1083\n",
      "梯度下降迭代800: 损失 J(θ) = 0.1082\n",
      "梯度下降迭代900: 损失 J(θ) = 0.1081\n",
      "梯度下降求得参数： [ 3.96103109  2.79948846 -1.9992547   1.13860197]\n",
      "真实参数 θ_true： [ 4  3 -2  1]\n",
      "正规方程求得参数： [ 3.97510695  2.79566239 -2.01002168  1.12661549]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 1000x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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r5MmTuv7669WmTRtFRkZ6LOcP86lTp47q1Kmj1NRUvfjii6pWrZoefvhh9/fw448/egzJe+edd+RwOPTUU0+517344ouSpCVLlmj8+PEqVaqU/Pz8tHz5cv3nP//RTTfdpJ9//llz5syR5Gw34eHhki693fzyyy/673//q1GjRqlkyZKZtruuDJbx+1y6dKkeffRR3XrrrRo4cGC27zFo0CD99NNP6tu3r06ePKmhQ4e6t6WkpGQ5DC0rSUlJ6ty5sxYsWKCOHTtesAcSQMFCsADgE4cPH3aPXb/QUKg777xTknOuQ3BwsNLS0nTjjTdecGy2azy4ayjHpbDZbBo4cKCuvvpqbdmyRUWLFnVvK1OmjKpVq6ZZs2Z5zE/IKC0tTePHj9err76qLl266MYbb9SAAQNUq1YttW3bVq+88orOnDmjwMBA2e127dy5U3fffbck5yVgJXlcZvRyrVq1SjfffLOCg4Pd6+Lj4yU5h8RkN/b//LkpjRo10pw5c5SSkpLtCbzkPIlPS0tTqVKl3EPVtm3bpvbt2+uVV15RlSpV5Ofn5z45lpzzGzKaMmWK+0Ta399fffr0UWhoqObNm5fp8rNnzpzx+F2dz+FwqFu3bgoNDdUtt9yiNWvWSHLetyIwMFAVK1ZUZGSk9u7dq3r16qlv377ucJATSUlJSktLU5MmTdSoUSN3QDl8+LAkZ1CRnO3jyy+/VPPmzVWnTh3368+ePasRI0bozTff1Msvv6ykpCTNnj1bFStWVIMGDTR+/Hh99913ioyM1MGDB7Vz50532N6xY4eKFSumsmXL5qjWm266SXPmzNF1112niRMnZrpUbGpqqqRz/37mzZunLl26qEKFCvrmm29y9O8qMDBQc+bM0R133OGeC+IKF6+//rr27NmTbRtMSEhQq1attHLlSj344IOaMmWK/P39c/QZAfgWwQKA16Snp+vXX39VXFycZs2apc8//zxHr1u1apUaNmwoh8Oh999/X9K5idoZ7d27V5LzPgRZbXcpWbKkwsLCstzWoUMHVaxY0X0syflX4vHjx3v0tmT0zz//qFmzZtq2bZuGDh2qwYMHa+LEiZKkt956S9dee6169uyp6dOn67bbbtNHH33knpshOe9xERMT43GyfTmMMTpw4IAaNGjgsd51b42IiIhMf/F3WbZsmXbt2uVx7w3J+dfw5ORkHTt2LNs5EZLUtGlTde7cWU899ZQ2btyobdu2qV69etq6datuuOEGderUSQMGDMj01/+M4WDy5MmaOHGi3nrrLY0fP16S1L1794u2l6xOVrt06aKWLVtq06ZN+uyzzzzm42ScPyA552TYbDZt374928/osmbNGj322GP64osv9OGHH3psc823+eGHH/T444/L399fu3btcgcNydkT1qpVKx09elQfffSRevTooQEDBqhIkSKaOXOmXnvtNfXr10+zZ89Wr1699NRTT+nnn39Wly5dJDnbTb169bI9UXex2Wzq1KmTxowZo4EDByokJESPPfaYe7vrIgtBQUFKSkrSU089pbCwMC1dulQRERHu/dq1a+dxAYSYmBh169bNPTelaNGiWrRokRo2bKjx48fr6aef1v79+zVq1Ci1b99eW7ZsuWidru0vvviixowZk+PPB8D3CBYA8tXu3bv13XffSZJ69Oih1NRUNW/e3P0X2dWrV7v3/fPPPxUSEuI+6dy5c6euvvpq9/aGDRvqzz//zPY9zz9pPN/IkSMzDWWSnEOtBg0apE8++cTjhOvJJ5/U+vXrNWTIEL344ouZTr5LlSqlpk2b6uOPP9ZNN92kr7/+Wvv27XNPmH700UfVtGlT95CVzZs3a8KECUpJSVFgYKC+++47NW7cONvPlZ3Tp08rNTU1U0BxnfCVK1fOHXjO17lzZ+3atStT74HrWCdOnMhRsJCcQ35iYmL09ddfq3r16pKktm3b6u6779acOXNUrVo1j6FmX3/9tfr16+d+7rpakqtuSRo9enSmG+odO3ZMTZo00YABAzx+Xy6hoaFKSkrS/fffr27dumU50d8lJCREMTEx+uWXX3L0GSXnJORdu3a5b9aX0U8//SSbzaYFCxYoKSlJQUFBCg4O9uhJqly5spo3b64XXnhB1apV0+TJk1WkSBH3VZsGDx6shx56yN1ubr31Vv3vf/+T5Pyr/tq1a7O8stbw4cM1fPjwC9b94osvavny5erVq5euuuoqdxB1XSzBbrcrKChIs2bNUvHixZWWlubRq+gayuVa57oaWFxcnOLi4hQYGKiqVatq6dKl+uuvv1SmTBl1795dpUqV0uTJk3XzzTdnqiklJUVjxozRoUOHVLRoUU2ZMuWCIRhAwUWwAJBvnnzySfdJkiR16tRJvXv31q233qrHH3880/4NGzbUPffc4/4r9fkmTZqU5eUvXZ5++mkdPnxYXbt2vehJyfmXvzx79qzeffddjRkzRqmpqRo9erT69evnvjLP3Llz9fDDD+uVV17RvHnzNH369EzH7N+/vyTnJXb79u2r6tWrq1+/fu5x8AEBAUpLS5O/v79atWql1157TUuXLlWZMmV06NAhj6v45IRrPHzGISKu78Z1xSGXsLAwhYaGuofnZMW1rUqVKh7rXT0Jl3KH5nLlyqlRo0aaP3+++8TXz8/PfSWntLQ0j/kNCQkJ2R6zfPnyHpeilaT//ve/MsZo9uzZat26te64444sXzt16tQc1V2/fn3NmzfPfWWsi9m4caMWLlyoLl266JZbbvHYdvbsWS1atEg9evTQ1KlTNWvWLD366KOZjmGz2fTqq69Kcg5r6tevnzp16qTq1au7203GOlq1aqXp06dr27Zt+u2335ScnJxlu+nYsaPHlcV27NjhcaUqPz8/TZ8+Xdddd53uv/9+bdq0SaVLl3b3WLiGPDVp0kRnzpzJFDaz47rqW1RUlPt33rlzZ/Xs2dOj58MlNjZWzz33nLu36JZbbiFUAIWVb+eOA7CyGTNmmAkTJpidO3dmukFet27dMt0IKzQ01OMqUDt27DCSzKpVq7J9rx9//NFIMtWqVTNVqlQxSUlJ2b7GdVWoO+64w0gynTp1MgcOHHBvz3hVqPT0dDN69GgTEBBgwsLCzFNPPeVxVSjl4EZhrmOnp6ebmJgY07x5c9O1a1cTHBxsEhISsq03oy+++MJIMk8//bR7XWJiovvKVue7/fbbjSRz8ODBTNscDocJDQ01FSpUyLTNdYfkHTt2XLSejFeFMsZ5taYWLVqYX375xePGd+PGjcvxVaGGDh3qvnv5+dauXWuKFCli2rdvb+rWrWtsNpvp06eP+4peWenWrZv7qlBZ+eyzz4wk89133130sxpjTLt27UxgYGCWd51+//33jSSzfv16c++995rq1au7b3KXkesO7BdbMn7+hIQEU6xYMfP444+b2267zVSqVMnjRo05uSpURnPmzDGSzMiRI40x537XJ06cyPIzDxkyxPj7+2c6jsvw4cONJDNx4sRM2zLWGR0dbVq1amV+++0306RJEyPJVKxY0Xz22WemUqVK3HkbKMSyvzMNAFymrl276tlnn1V0dHS2+x4/flzx8fHuv3BeiqSkJD3zzDMqW7asFi9erCNHjrj/EpwTr732mhYtWqQ5c+Z4DPdJSkpyD3uy2Wx6+eWXtXLlSo0bN06lS5f2OEZCQoLWr1+vwMBAvf3220pISHAvDz74oGrUqOH+i7vNZtPTTz+tZcuW6csvv1SPHj08hv3kxG+//SZJuvbaa93rgoODFRIS4tEb4NK+fXtJ0qxZszJtW7RokeLj49WhQ4dM21zHOv/zZsUYo9TUVCUlJWnjxo0XvOfAVVddJWOMe8mqpouJjY1Vq1atFBkZqc8//1w//fST+vXrp3fffVc33XST+7u5VK1atZK/v79mzJiRaduKFSvcc1VWrVqlhQsX6qmnnsrUw3Py5EmNGDFCjRo1Ut26ddW/f3/t2bNHo0ePznTM6OhoJSQkaP78+ZKcN8DL2G4aNWrkMUSuWLFi6tatm6ZMmaI1a9aoT58+uZp/0KlTJ8XGxrqHBbp6vDIO18po6NChatSokTp37uy+apfk/L2/+uqr7vlFzzzzTKbXZlVnqVKltG/fPg0bNky7d+9Wt27dLvp5pk2bpsWLF2eawA+gAPFlqgFwZTh79my2PRbvvfeekWQ+//xz97qc9FikpKSYe+65x0gys2fPNsac+6v4e++9d9G6XD0WLn/++afp16+fGTFihOnXr5/x8/MzL7/8cpavPf8+FsY4eziKFCliFi1a5F63ZMkSY7PZzBdffOGx74kTJ0xAQECOegPOFxcXZ6Kjo01AQIBHD4sxxtSrV89UrVo102v++ecfExYWZsLCwjzux3DkyBFTtWpVU6RIkSz/+t60aVMTERGRbU2jR482lSpVMuXLlzd2u934+fmZFStWZNljcdVVVxljnPe1SE9PN6+++qopVapUpmOe32MRHx9vXnjhBePv72+qVq1q9u/f77H/N998Y0JDQ01wcLD57LPPMh0vux4LY4zp2LGjCQ4ONkeOHHGvO378uLsnID093dx0000mJCTEYx/X5+nQoYPx9/c369atc69/9NFHjb+/f6Z7ixjjbL/VqlUz4eHh7vtRGGPMpEmTjM1mM2vWrPHY33VPmCJFiphTp055bLvUHovz9e/f39hsNo/ehfMdPXrU1KpVy4SHh5vY2Fhz6NAh07JlS+Pn52eGDx9+0eO7uHosjDEe95VxbbtQj0Xr1q1NkSJFLlofAN8iWADId1kFi48++siMGDHCGGPM77//bkqXLm0CAwPdQ5J27txpjhw5Ynr27Om+od75Dh8+7B7GdP5N3Lp162Ykmb59+15weMz5wSIuLs4EBAQYm81m7Ha7ueOOO8zRo0ezfG1WweKPP/4wjz32mAkICDA33HCDef31101ISIjHDdGMcZ5MdejQwT3cpVmzZtkO3Tp16pRp0KCBeeSRR0xUVNQFb1z3wgsvGEnmr7/+yrRtzpw5xt/f3wQFBZl77rnHPPLII6Z06dLGZrOZjz/+ONP+ycnJJjg42Nx3330Xrc2Yc0Oh5s2bZ9577z33jfYGDhxoJJkNGzYYYzyDRcbf+T333JPpmD169DD+/v7uE0nXsJl77rnHnDx5Mss6duzYYapVq2YaNmyY6aQ1J8Fi1apVmW7I5rop46xZs9wB+KWXXvJ4XVpamunZs6eRlOkE2xUEixUrlunmc8YYs2nTJtOpUydjs9lMgwYNzLBhw4y/v78ZNWqUx37//vuvueWWW9zt5uGHH87VUKjzPfbYY9neqNAYZ1ts1KiR8ff3N2FhYaZUqVIeNwLMTsZgkdW2CwWLmjVrZhmaARQcBAsA+e7MmTNGkpk+fbrH+rS0NDN9+nQTHh5uwsLCzJYtW8y0adNMxYoVjb+/v3nqqac87jTs4nA4zAcffGBKly5t/P39zdixYzPtk5aWZvr06WMkmapVq5rp06cbh8Phsc/5weJSZBUsXDZu3GjCw8PdJ4Bjx451z6FIS0szPXr0MJJMnz59zEsvvWQkmbvuuuui8ywSEhJMxYoVTWBgoKlRo4Z59913s9xvxYoVRpKZMGFClttXrlxpmjdvbooXL26KFy9umjRpkuVf0o0x7juZZ/XX//OdP8fC9V5+fn4mKirK1K1b1xw/ftxs2bLF3XuzYMECM2XKFDN//nyPOQjp6emmX79+RpKx2+3m4YcfNvHx8Wb37t0evUEXEhcXl2UgzEmwMMaYJ554wkgyr732mjHm3O96//795sUXXzTFixf3aJcnT550B8VHHnkky7+o79ixw5QqVcrY7fYsQ5wxzgATHBzs/tyffPKJ+3s5e/asadOmjZFk3nzzTfddunv27GlSUlKMMeeCxYWWiwUL153Nq1evftHvZsOGDWbAgAEmPDzc+Pv7G7vdbsLCwsyzzz5r1q5da9LS0i7+5ZqLB4vq1aubWrVqZVp/+vRpExgYaNq1a5ft8QH4DsECQL5ZvXq1+fDDD90n+N9++605fPiw+e9//2uee+4591/e69SpY3777Tf36/79918zePBgExgYaEqUKGHGjRtn0tLSTFxcnBk3bpypXLmykWSqV69uVq5cedEa5syZYypUqGAkmfLly5v+/fub9evXG2PO9WrkZslo+/btZvDgwaZEiRKmaNGi5vXXXzedO3c2NpvN1K5d2xw7dsw0b97cSDKPPvqo+wS0e/fuRpKpUqWK+fHHH3P9vdetW9dUq1YtRyd5F9O4cWNTrly5HE2EPz9YnDlzxlSpUsX06tXL/PXXXyY6OtpERESYAQMGmEmTJplp06aZ6dOnm+nTp5vPP//cTJ482bz//vvm0KFD7onxr776qlm5cqUpXry4CQ8PN48//rgZP368+fzzz8306dPNzJkzzcyZM82MGTPcx/n000/NpEmTzHvvvWcmTpzocZKf02Dx77//mptvvtlIMtddd50JCQkxNWvWdG/POAF+zpw57nbcp0+fi37nP//8s4mIiDCSTIcOHUx6erpJT08369evN7179zbBwcEmPDzcjB8/3rRo0cK93969e03t2rU9ekOSk5Pd+9SuXdts377dHSzatGljJkyY4F5c//4yBou2bduap59+2gwfPty88cYb7tDSq1cv9z5paWlm165dZurUqaZHjx4mOjraSDIlS5Y0vXv3Nnv37jUHDx40ffr0MaGhoUaSCQ8PN3fffbcZMmSImTlzplm5cmWmkHexYNGxY0d3HePGjTPjxo0zb731lmnUqNEFJ4YDKDgIFgDyzZQpU4zNZjN+fn6mUaNG5uzZs2b79u2mSJEiJiQkxLRt29Z88803FzwZ27x5s6lTp4556KGHjMPhMHXq1DGSTOnSpc2bb76ZoxNeY5x/7R8zZowpX7688fPzc1/15/vvvzcffPDBZS2uEzFjnEOyqlataiSZsLAw069fP3P48GH3+69bt87ExsaamJgYY7PZzODBgz0+c1pamhkyZIix2Wyme/ful/t1u82dO9dIMjNnzrzsY7iGBP3nP//J0f7nB4ulS5ea+vXru39HJ06cMC+88IKpXr26e27J+UtYWJhJTEw0EydOND169HAf6+DBg6Zfv37mmmuuMcWLFzc2my1Hoe/ee+/1qDGnwcIYZzB65plnTMmSJU1kZGSWV4pKSUkxt912mylZsmSOv+s///zT1K5d23z55Zdm06ZNpmLFikaSKVu2rBk2bJjHvImlS5ea2NhYU7JkSVOkSBHz/vvvexwrKSnJ3bsybNiwSxoKVatWLY/vKjAw0HTs2NH8888/xhhnD0FkZKR7e0REhOnWrZuZO3dulv/uEhMTzRdffGEeeughd5B39bxs2bLFY9+LBYs9e/aY22+/3QQFBXnUV6pUKdOrV69MvY4AChabMVxeAYB37dq1SzExMSpSpEi2+6ampio9PV1FihTR3r17tWTJEnXv3j3TvRpyIjU1VVu3blXt2rUvp+yLGjp0qK6++mrdddddF6xtxowZKlmypNq2bZvl9tjYWN18880XvCv4pXjwwQcVGxurbdu2ZXnvgItJTExUrVq1VLZsWf3www8e98q4FMaYC17lJzExUcnJyUpNTXXvFxQUpOLFi8vhcMhms2W6EWFG6enp7iXj/8b8/Pxks9nk5+cnPz/PCx+ePn1aycnJl/x9XMzhw4fl5+ensmXL5vg1qampCggIUHp6ugYMGKCmTZuqdevWF7x3xjvvvKP69etneWM5SZo3b57uvPNOBQQEaM+ePSpVqpRKlSqVbR0pKSlKSkpSSkqKSpYsmen3vHjxYu3fv18NGzbUddddd0lXoPrzzz+1detWBQYGqlWrVjl+HYDCjWABABZ0+vRpjR8/XrfffvsFbxx3IevXr9fChQv12GOPqVKlSvlUIQDAaggWAAAAAHKNG+QBAAAAyDWCBQAAAIBcu/DMOItJT0/X33//reLFi1/SBDQAAADgSmWMUUJCgipUqJDpohjnu2KCxd9//62oqChflwEAAAAUOgcOHFBkZORF97ligkXx4sUlOb+U0NBQn9TgcDi0dOlStWzZ8oKXFcSVgbYAF9oCXGgLyIj2ABdft4X4+HhFRUW5z6Uv5ooJFq7hT6GhoT4NFiEhIQoNDeU/Elc42gJcaAtwoS0gI9oDXApKW8jJVAImbwMAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwL8HUBV4pKlaQDBwJVunRLHT7s62oAAACAvEWPhZekp/u6AgAAACD/ECy8xO//v2ljfFsHAAAAkB8IFl5iszl/GmPzbSEAAABAPiBYeAk9FgAAALAygoWX0GMBAAAAKyNYeAk9FgAAALAygoWX0GMBAAAAKyNYeAk9FgAAALAygoWXuHos0tPpsQAAAID1ECy8xI9vGgAAABbG6a6X0GMBAAAAKyNYeAk9FgAAALAyTne95FyPhW/rAAAAAPIDwcJLzvVYMBQKAAAA1kOw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BLuYwEAAAArI1h4Scb7WBjjuzoAAACA/ECw8BJbho4KggUAAACshmDhJfRYAAAAwMoIFl6SsceCK0MBAADAaggWXsJQKAAAAFgZwcJLGAoFAAAAKyNYeAlDoQAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBS5YbN68WXXq1NHq1avd6/7880/dc889Cg0NVenSpdWpUyf9+eefPqzy0tFjAQAAACsrMMFiw4YN6ty5s+rXr6+NGzd6bHvppZdUpUoV/fDDD/rvf/+r/fv3q3379kovRH/6p8cCAAAAVhbg6wJc5s6dK7vdroULF6pZs2Ye2958801FRUW5n0+cOFENGjTQ77//rquuusrbpV4WeiwAAABgZQUmWIwcOVI2m0379+/PtC1jqJCkoKAgSVJaWpo3SssT9FgAAADAygpMsLBlPPPOxscff6zIyEjVqFHjgvskJycrOTnZ/Tw+Pl6S5HA45HA4Lr/Qy2Sz+cs18iwlxSEflIACxNUGfdEWUbDQFuBCW0BGtAe4+LotXMr7FphgkRPGGI0YMUKTJk3SN998o4CAC5c/evRoDR8+PNP6pUuXKiQkJD/LzNKxY7dIKidJWr58hcLCUrxeAwqe2NhYX5eAAoK2ABfaAjKiPcDFV20hMTExx/vajClYI/7379+vmJgYrVq1Sg0bNnSvP3XqlLp166bly5drxowZat++/UWPk1WPRVRUlOLi4hQaGppv9V9Ip07+WrjQ2WOxb1+iKlYM9HoNKDgcDodiY2PVokULBQbSFq5ktAW40BaQEe0BLr5uC/Hx8QoPD9fp06ezPYcuFD0Wx48fV5MmTRQSEqKNGzeqatWq2b7GbrfLbrdnWh8YGOiTX4q/f8bHvqkBBY+v2iMKHtoCXGgLyIj2ABdftYVLec9CESx69eqlsLAwff/99+6J24UNV4UCAACAlRX4YJGYmKh58+bpzTff1MGDBz22lSxZUqVLl/ZRZZeGq0IBAADAygrMDfIuJC4uTqmpqerXr5+qV6/usYwePdrX5eUYPRYAAACwsgLXY1G5cmVlnE9eqVIlFbD55ZeFHgsAAABYWYHvsbAKeiwAAABgZQQLL6HHAgAAAFZGsPASeiwAAABgZQQLL6HHAgAAAFZGsPASeiwAAABgZQQLL6HHAgAAAFZGsPCSjMGCHgsAAABYDcHCSzIOhaLHAgAAAFZDsPASeiwAAABgZQQLL2HyNgAAAKyMYOElTN4GAACAlREsvIQeCwAAAFgZwcJL6LEAAACAlREsvMSPbxoAAAAWxumul3j2WNguvCMAAABQCBEsvIQ5FgAAALAygoWXMMcCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8JKMwYIeCwAAAFgNwcJLGAoFAAAAKyNYeAlDoQAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVkaw8BJ6LAAAAGBlBAsvoccCAAAAVlbggsXmzZtVp04drV692mP9Bx98oJiYGAUHB+uOO+7Q3r17fVTh5aHHAgAAAFZWYILFhg0b1LlzZ9WvX18bN2702PbVV1+pX79+GjFihFavXi2Hw6G77rpL6YXoDN2vwHzTAAAAQN4rMKe7c+fOld1u18KFCzNtGz16tHr27KmHH35YdevW1ccff6zffvtNK1as8EGll4ceCwAAAFhZgQkWI0eO1LRp01SlShWP9adOndLGjRvVpk0b97qaNWuqfPny+vnnn71d5mVjjgUAAACsLMDXBbjYMv5JP4N9+/ZJkmJiYjzWV6pUSQcPHrzg8ZKTk5WcnOx+Hh8fL0lyOBxyOBy5LfeSpafb5Pq6HY40ORykiyuZqw36oi2iYKEtwIW2gIxoD3DxdVu4lPctMMHiQs6cOSNJCgkJ8VgfEhLiERzON3r0aA0fPjzT+qVLl2Y6ljds21ZJUm1J0m+/7dCiRX96vQYUPLGxsb4uAQUEbQEutAVkRHuAi6/aQmJiYo73LfDBwm63S5JSUlI81iclJV00IAwcOFD9+/d3P4+Pj1dUVJRatmyp0NDQ/Cn2IuLizvXI1Kx5jdq2vdbrNaDgcDgcio2NVYsWLRQYGOjrcuBDtAW40BaQEe0BLr5uC65RPzlR4INFxYoVJUkHDhxQ1apV3esPHDigzp07X/B1drvdHUoyCgwM9MkvJeNb+vn5KzDQ3+s1oODxVXtEwUNbgAttARnRHuDiu3PYnL9ngZm8fSEVK1ZU5cqVPbp/du/erYMHD6pZs2Y+rOzScFUoAAAAWFmB77GQpP79+2vgwIGqVauWYmJi1K9fP7Vr107XX3+9r0vLMa4KBQAAACsrFMHi2Wef1fHjx/X0008rKSlJd999tyZOnOjrsi4JPRYAAACwsgIXLCpXrixz3p/0bTabRowYoREjRvioqtzLGCzosQAAAIDVFPg5FlaRcSgUPRYAAACwGoKFl9BjAQAAACsjWHgJk7cBAABgZQQLL2HyNgAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKPBQAAAKyMYOEl9FgAAADAyggWXkKwAAAAgJURLLwkY7BgKBQAAACshmDhJQQLAAAAWBnBwksIFgAAALAygoWXZAwWaWm+qwMAAADIDwQLL/H3P/eYHgsAAABYDcHCSzyHQtkuvCMAAABQCBEsvIQ5FgAAALAygoWXECwAAABgZQQLL2HyNgAAAKyMYOElTN4GAACAlREsvIShUAAAALAygoWXECwAAABgZQQLLyFYAAAAwMoIFl7C5G0AAABYGcHCS5i8DQAAACsjWHgJQ6EAAABgZQQLLyFYAAAAwMoIFl6SMVgY47s6AAAAgPxAsPASJm8DAADAyggWXsLkbQAAAFgZwcJLmGMBAAAAKyNYeAnBAgAAAFZGsPASggUAAACsrNAEi4SEBD3xxBMqVaqUihcvrs6dO+vw4cO+LivHmLwNAAAAKys0waJ3795auXKl/vvf/+p///uf9u/frwceeMDXZeUYk7cBAABgZQG+LiCnfvnlFz377LO64447JEmDBw8uVMGCoVAAAACwskLTY9GlSxd9+eWXOnr0qE6dOqVPP/1UXbp08XVZOWaznXtMsAAAAIDVFJoei0GDBmnZsmUqV66cbDabatasqbVr115w/+TkZCUnJ7ufx8fHS5IcDoccDke+15sVP78ApafblJZmfFYDCgbX7592ANoCXGgLyIj2ABdft4VLeV+bMcbkYy155rHHHtOaNWs0fvx42e12vfjiiypTpowWLVqU5f7Dhg3T8OHDM62fOXOmQkJC8rvcLN1zT3ulpfmpSpVTevvtFT6pAQAAAMipxMREde3aVadPn1ZoaOhF9y0UwWL79u269tprtW7dOtWrV0+SdODAAUVHR2vp0qVq3rx5ptdk1WMRFRWluLi4bL+U/FK8eICSk2264YZ0rV/PpaGuZA6HQ7GxsWrRooUCAwN9XQ58iLYAF9oCMqI9wMXXbSE+Pl7h4eE5ChaFYijU1q1bJUm1atVyr4uKilJ4eLi2bNmSZbCw2+2y2+2Z1gcGBvrsH6ifnzPDGWPjPxKQ5Nv2iIKFtgAX2gIyoj3AxVdt4VLes1BM3q5YsaIkZ8+Fy+HDhxUXF+feVhi4rgzF5G0AAABYTaEIFg0aNFCdOnXUvXt3LV++XD/++KPuu+8+VapUSe3atfN1eTlGsAAAAIBVFYpgYbPZtHjxYl1zzTXq1KmTWrdurVKlSun7779X0aJFfV1ejrmCBXfeBgAAgNXkao7F6dOndeTIEZ08eVKhoaEqW7asSpcunVe1eYiIiNCMGTPy5dje4rr7Nj0WAAAAsJpLDhZ//vmnJkyYoCVLlmjHjh2SJGOMbP9/B7iqVauqVatW6t27t2rUqJG31RZyrh6Lgn8dLgAAAODS5HgoVFJSkp555hlVr15dixYtUqtWrTR37lz9/PPP2r17t9auXat58+apU6dOWrVqla699lr16NFDiYmJ+Vl/ocIcCwAAAFhVjnssateuraJFi+qbb75R27ZtL7hfu3btNGbMGC1btkxDhgxRnTp1tHPnzjwptrAjWAAAAMCqctxj0alTJ/38888XDRUZNW/eXKtXr9YDDzxw2cVZDZO3AQAAYFU5DhajRo1SQMC5Do60tLRshzn5+flp6NChl1+dxTB5GwAAAFaV42CRnJysiRMnqlmzZipTpoyKFCmi4sWLKyAgQDExMXrwwQf13Xff5WethR5DoQAAAGBVOQoWx44dU926ddWnTx9t2LBBN954ox544AEZY9SkSRPFxMRo6dKlatmypR566CGlMdYnSwQLAAAAWFWOgsVLL72kvXv3atKkSTp+/LiWLVumDz/8UJI0YsQIff/99/r777/16aef6ptvvtEbb7yRr0UXVgQLAAAAWFWOgsW3336rQYMG6fHHH3fPs3Ddt8IlMDBQ3bp106BBg/Tpp5/mfaUW4PrK6NABAACA1eQoWJw5c0Y33HBDjg543XXX6dChQ7kqyqqYvA0AAACrylGwuOaaa7Rw4cIcHXDFihWqVKlSroqyKoZCAQAAwKpyFCz69u2ryZMnq2fPntq3b5/HNteQqISEBL3++uuaMGGCnn766byv1AIIFgAAALCqHN15++GHH9bff/+toUOHavLkySpbtqzKlCkjm82mXr16KTU1VXv27FFqaqr69++vvn375nfdhRLBAgAAAFaVo2AhOa8M1bVrV82YMUM//fST9u/fr5iYGKWmpioyMlKdOnXSgw8+qKuuuio/6y3UuPM2AAAArCrHwUKSoqKi9PLLL+dXLZbn728k2eixAAAAgOXk+M7bTZo00cGDBy/p4EeOHFGLFi0uuSirYigUAAAArCrHwSIyMlLXXnutBg4cqCNHjlx03xMnTmjo0KG65pprFBERkesireJcsLBdfEcAAACgkMnxUKjp06friy++0JAhQ/TWW2+pVq1aatSokSpUqKASJUooPj5ehw8f1urVq7V+/XpVqFBB48aNU7du3fKz/kLFL0OMM+bcDfMAAACAwu6S5ljcf//96tKlixYsWKAlS5Zo2bJlOnz4sE6fPq3ixYurbNmyql+/vvr166eOHTu679INp4zBIi1N4usBAACAVVzyqa3NZtNdd92lu+66Kz/qsTTXnbcl5lkAAADAWnI8xwK5l7HHgmABAAAAK8lxj8XKlSsvfJCAAEVFRSkyMtJ9J25kRrAAAACAVeU4WDRp0iTb0FCmTBm98sor6t27d64LsyKCBQAAAKwqx8FiypQpF9yWnp6uuLg4LV++XM8995wSExP10ksv5UmBVnL+5G0AAADAKnIcLHJy2dgXXnhB/fr10/vvv0+wyAKTtwEAAGBVeT55u1GjRtneQO9KxVAoAAAAWFWeB4vAwED16dMnrw9rCRmnqBAsAAAAYCV5fou2du3aqV27dnl9WEugxwIAAABWxX0svIjJ2wAAALAqgoUXMXkbAAAAVkWw8CKGQgEAAMCqCBZeRLAAAACAVeUqWJw5c0Y1atTQP//8k2nbqFGj9MYbb+Tm8JZDsAAAAIBVXVKwCAkJ0Z49e9zP09LStGfPHqWmpmbad9asWfr+++9zX6GFMHkbAAAAVnVJwSIpKUnp5/2p3Zbx5gz/b+XKldq+fbv69euXu+oshsnbAAAAsKp8mWMxePBg1atXT61bt86PwxdaDIUCAACAVeX5DfLGjx+vX375RRs2bMjrQxd6BAsAAABYVa6DhTHG/fiLL77QSy+9pA8//FBXX311bg9tOQQLAAAAWNUlD4U6f06FzWZTXFycevfure7du2vKlCl69NFH86xAK/HzOxfCmLwNAAAAK7loj8W2bdvUqFEjFSlSRHa7XTabTXfeeaeKFSsmu90uf39/GWNUp04d3XXXXfrtt99UtWpVb9Ve6DB5GwAAAFZ10WBRrlw5DRkyRJLz0rIvvPCCWrRoodDQUJ09e1b//POP1qxZo7S0NK1bt05r164lWFwEl5sFAACAVV00WISHh+u5555zP3/hhRfUt29f1ahRQ5J06tQpzZgxQ5s2bdLnn3+ubt26aeXKlfrwww/ztejCKmOPBcECAAAAVpKryds2m03GGJUpU0Zjx45VkyZNdM899ygkJERvv/12XtVoGQQLAAAAWFW2k7d37dql999/X6dPn85ye8bJ3G3bttXHH3+sd955R/Pmzcu7Ki2CoVAAAACwqmyDxc6dO/Xqq6+qQoUKstlsOnv27EX3f+ihh3TPPffomWeeUWJiYp4V6nL8+HF1795dpUuXVnBwsDp06JDn75FfAjL0D6Wm+q4OAAAAIK9lGyzuvvtuHT16VJ9++qnq1q2rpk2baty4cUq9yJnx2LFjdezYMb3zzjt5WmxCQoIaNWqkw4cP6+uvv9ZPP/2kBx98ME/fIz8xFAoAAABWlaP7WAQEBKhLly5at26d3n//fY0dO1YtW7aUMcbjBnkulStXVpcuXfTOO+8oJSUlz4odM2aM0tPTtWDBAjVq1Ei1atXSfffdl2fHz28ECwAAAFjVJU/evv/++9WsWTOdOHFC/v7+io6Oln/GM+b/9+STT+rs2bNZBo/L9dlnn2nQoEEqUqRInh3TmwgWAAAAsKrLuipUmTJlVKZMGUnSvn37stynQYMGqly5sux2++VXl8Fff/2lv//+W6GhoWrSpIm2bt2qa665RuPGjdNNN92Uaf/k5GQlJye7n8fHx0uSHA6HHA5HntR0qWw2I8mZLpKSUuVw5F3oQuHiaoO+aosoOGgLcKEtICPaA1x83RYu5X1t5jK7FOLj4z3uceESExOjV199VW+//bbGjRunP/74I096GNauXatbb71VN9xwgwYPHqzIyEi9/vrrWrNmjX7//XeVKlXKY/9hw4Zp+PDhmY4zc+ZMhYSE5LqeyzF3bjVNnXqtJOmll9apfv3DPqkDAAAAyInExER17dpVp0+fVmho6EX3zbbH4sSJE4qIiPBYFx0drZ9++kmfffaZ+vbt67GtePHiOnTokIYNG6aXX345z4YtuSaLP//88+55FVOnTlVERIQWLlyoRx55xGP/gQMHqn///u7n8fHxioqKUsuWLbP9UvLL9u3nMtyNN9ZR27b0WFypHA6HYmNj1aJFCwUGBvq6HPgQbQEutAVkRHuAi6/bgmvUT07kaCiUMUYbN26UMUZ16tTRtGnTJDnvYTFu3LhM+997772qXbu2Bg0alONCsuMKN9WqVXOvK1mypCIiInT06NFM+9vt9iyHYQUGBvrsH6jdfm5ihc0WIP47AV+2RxQstAW40BaQEe0BLr5qC5fynjkKFjabTTfeeKP7efXq1S84KXvx4sVauHChtmzZkuMicqJq1aqKiIjQzz//rNtuu02SFBcXp2PHjqlGjRp5+l75JePkbe5jAQAAACu5rMnbGe3atUsTJkxQaGiorrrqKo0cOVIvvfRSnp/s+/n5qX///ho5cqQqVKigKlWqaPDgwapRo4batm2bp++VX7gqFAAAAKwq18HCGKNTp05p3759+vzzz3X48OE8vcRsRi+++KISExPVt29fxcfHq2nTplq4cGGh6SL09z/3vRAsAAAAYCW5DhY1a9bU9OnTJUlpaWmaMmWKevfuLT8/Pw0bNiy3h/dgs9k0fPjwLK/2VBgEZPi2CRYAAACwkhwHix07dig9PV02m0379+9XdHR0pn38/f31+OOPq1ixYnr44YfVuXNnXXPNNXlacGHml+E+58yxAAAAgJXk+KpQ1113nXuIU/fu3bV8+XIZYzRixAiPfSMiIvTUU09p3Lhx+s9//qNPPvkk76supJhjAQAAAKvKNliULl060x33bDabEhISdPfdd2vTpk0ecyoqV64sSXriiSf04osvavLkybLZbHlbdSFFsAAAAIBV5ajHwv//z4i7du2qnj17qnHjxgoLC9Ozzz6rjz76SLNnz870mttvv12SdOjQIUVGRuZhyYUXcywAAABgVX7Z73LOgQMH9O+//7qfV6lSRXPmzNHff/+dad+rrrpKO3fuJFRkwH0sAAAAYFXZ9lgMGDDAfbO73377TYMHD9b48ePd2202m9q3b6/SpUt7vC4kJETdunVTx44d87biQoyhUAAAALCqbINF3bp1VaZMGUnS77//rhtvvFE1a9Z0b09NTdX+/fvVuXNnj9etWbNGjzzyiBISEvK45MKLYAEAAACryjZYPPDAA+7HCxcu1H333edxp+vo6Gg98cQTeu6552S3293rt27dqhtvvDGPyy3cMs6xYCgUAAAArOSS5li0bdtWUVFRHusaN26sJk2a6MCBAx7rQ0JC9Oqrr+a+QguhxwIAAABWdUl33h44cGCmdeXLl9eCBQsyra9atWqhvUN2fiFYAAAAwKouqccCuUOwAAAAgFURLLyIORYAAACwKoKFF9FjAQAAAKsiWHgRwQIAAABWRbDwIn9/435MsAAAAICVECy8KGOPBXMsAAAAYCUECy9iKBQAAACsimDhRQQLAAAAWBXBwosyXm6WYAEAAAArIVh4EXMsAAAAYFUECy9iKBQAAACsimDhRQQLAAAAWBXBwosyzrFgKBQAAACshGDhRfRYAAAAwKoIFl5EsAAAAIBVESy8iGABAAAAqyJYeBFzLAAAAGBVBAsvoscCAAAAVkWw8CKCBQAAAKyKYOFFBAsAAABYFcHCi2w2yc/PSGKOBQAAAKyFYOFlrmBBjwUAAACshGDhZQQLAAAAWBHBwssIFgAAALAigoWXMccCAAAAVkSw8DJ/f3osAAAAYD0ECy/z80uXRI8FAAAArIVg4WUBAc4eC4fDx4UAAAAAeYhg4WX+/s4eC4IFAAAArIRg4WX0WAAAAMCKCBZeRo8FAAAArIhg4WWuq0IRLAAAAGAlBAsvI1gAAADAigplsJg6dapsNpumT5/u61IuWUCAcyhUerpzAQAAAKyg0AWLpKQkDRkyxNdlXDbXHAuJe1kAAADAOgpdsBg5cqTq1avn6zIum2solMRwKAAAAFhHoQoWW7Zs0QcffKBx48b5upTL5hoKJREsAAAAYB0Bvi4gp5KSkvTggw9q8ODBioyMzHb/5ORkJScnu5/Hx8dLkhwOhxw+OqN3OBwePRaJiQ4VLeqTUuBjrjboq7aIgoO2ABfaAjKiPcDF123hUt630ASLfv36KTw8XM8991yO9h89erSGDx+eaf3SpUsVEhKSx9XlXEDAuWFc//vf9ypVKslntcD3YmNjfV0CCgjaAlxoC8iI9gAXX7WFxMTEHO9bKILF5MmTNXfuXG3atEl+fjkbvTVw4ED179/f/Tw+Pl5RUVFq2bKlQkND86vUi3I4HBo79qT7eaNGd6hSJZ+UAh9zOByKjY1VixYtFBgY6Oty4EO0BbjQFpAR7QEuvm4LrlE/OVEogsWoUaN04sQJxcTEeKx/7LHHNHLkSO3atSvTa+x2u+x2e6b1gYGBPv0HmnGOhRQo/ltxZfN1e0TBQVuAC20BGdEe4OKrtnAp71kogsWyZcsyje+6+uqrNWrUKHXq1MlHVV0ergoFAAAAKyoUwaJq1apZri9fvvwFtxVUXBUKAAAAVlSoLjdrBfRYAAAAwIoKRY9FVowx2e9UANFjAQAAACuix8LL/PzosQAAAID1ECy8LCDgXLBITfVhIQAAAEAeIlh4mb8/Q6EAAABgPQQLL2OOBQAAAKyIYOFlXBUKAAAAVkSw8DJ6LAAAAGBFBAsvo8cCAAAAVkSw8DKCBQAAAKyIYOFlGa8KxeVmAQAAYBUECy/LeB8LeiwAAABgFQQLL+M+FgAAALAigoWXcVUoAAAAWBHBwsuYvA0AAAArIlh4GcECAAAAVkSw8DKuCgUAAAArIlh4WcY5FikpPiwEAAAAyEMECy/LGCySk31YCAAAAJCHCBZeVqQIwQIAAADWQ7DwssBAggUAAACsh2DhZQQLAAAAWBHBwssCAtLcjwkWAAAAsAqChZdl7LFISvJhIQAAAEAeIlh4GUOhAAAAYEUECy/jqlAAAACwIoKFlzHHAgAAAFZEsPAyf3/J399IIlgAAADAOggWPmC3O38yeRsAAABWQbDwAVewoMcCAAAAVkGw8AGCBQAAAKyGYOEDQUHOnwQLAAAAWAXBwgeKFHH+JFgAAADAKggWPsBQKAAAAFgNwcIH7Hbn5WaTkiRjfFwMAAAAkAcIFj7g6rGQJIfDd3UAAAAAeYVg4QOuydsSw6EAAABgDQQLH8jYY0GwAAAAgBUQLHzAdVUoiWABAAAAayBY+EDGHoukJN/VAQAAAOQVgoUPMBQKAAAAVkOw8IGQkHPXmD171oeFAAAAAHmEYOEDISHnHv/7r+/qAAAAAPIKwcIHCBYAAACwGoKFD2QMFomJvqsDAAAAyCuFKlhs2bJFLVu2VEhIiMqVK6dHH31UJ06c8HVZl6xo0XOP6bEAAACAFRSqYPHss8+qSZMm+vnnn/XJJ59oxYoVeuSRR3xd1iUrWvTc5G2CBQAAAKwgwNcFXIoZM2YoKipKknTDDTfo9OnTevjhh5WYmKiQjOOLCrjg4HOPGQoFAAAAKyhUPRauUOESFBSk9PR0H1Vz+RgKBQAAAKspVD0WGRlj9Mknn+iWW27JsrciOTlZyRnuPhcfHy9JcjgccjgcXqszI9f72u2pcn318fFpcjgKXzhC7rjagq/aIgoO2gJcaAvIiPYAF1+3hUt5X5sxxmS/W8HicDj09NNPa8aMGVq5cqVuuummTPsMGzZMw4cPz7R+5syZPh82tXt3Cb34YmNJUtu2e/Xkk1t9Wg8AAACQlcTERHXt2lWnT59WaGjoRfctdMHi4MGD6tKli/bu3auvv/5at956a5b7ZdVjERUVpbi4uGy/lPzicDgUGxurihVbql4950SLbt3S9fHHaT6pB77jagstWrRQYGCgr8uBD9EW4EJbQEa0B7j4ui3Ex8crPDw8R8GiUA2F2r17t5o2barrr79emzdvVkRExAX3tdvtstvtmdYHBgb6/B9oaOi5rz0pyU+BgYVqqgvyUEFojygYaAtwoS0gI9oDXHzVFi7lPQtVsOjatavq16+v2bNny8+v8J6MM3kbAAAAVlNogsXu3bv166+/6uWXX9bevXs9tpUpU0ZhYWE+quzSESwAAABgNYUmWBw5ckSSdN9992XaNmHCBD377LPeLumycR8LAAAAWE2hCRaNGjVSIZtnfkF+fs5wcfasdOaMr6sBAAAAcq/wTlQo5Fwjt/7/9hoAAABAoUaw8JESJZw/T53yZRUAAABA3iBY+IirxyIhQUrjNhYAAAAo5AgWPuLqsZAYDgUAAIDCj2DhIxmDBcOhAAAAUNgRLHyEYAEAAAArIVj4SMb7+Z0+7bs6AAAAgLxAsPAReiwAAABgJQQLHyFYAAAAwEoIFj6SMVgwFAoAAACFHcHCR0qWPPf4xAnf1QEAAADkBYKFj0REnHt87Jjv6gAAAADyAsHCR8qWPff4yBHf1QEAAADkBYKFj2TssTh61Hd1AAAAAHmBYOEjgYFSqVLOxwQLAAAAFHYECx9yDYciWAAAAKCwI1j4kCtYJCZKZ874thYAAAAgNwgWPlSu3LnHhw/7rg4AAAAgtwgWPhQdfe7xvn2+qwMAAADILYKFD1Wpcu7x3r2+qwMAAADILYKFDxEsAAAAYBUECx8iWAAAAMAqCBY+FBUl+fs7H+/e7dtaAAAAgNwgWPhQYKB09dXOxzt2SElJvq0HAAAAuFwECx+rXdv5MzVV2rbNt7UAAAAAl4tg4WN16px7/OuvvqsDAAAAyA2ChY/deuu5x99957s6AAAAgNwgWPjYTTdJJUo4H8fGOodEAQAAAIUNwcLHAgKkli2dj0+dkhYv9mk5AAAAwGUhWBQAjzxy7vH48ZIxPisFAAAAuCwEiwKgdWspJsb5+Pvvpa++8m09AAAAwKUiWBQA/v7S6NHnnnfrJs2e7bt6AAAAgEtFsCggOneWHnzQ+TgpSerSRWrf3tmDkZ7u29oAAACA7BAsCgibTfr0U6l793PrFi6UmjWTKleWnn5amjdPSkjwVYUAAADAhREsCpAiRZzhYsoUqWLFc+sPHJA++EDq0EEqXVq67TbphRecQeP4cZ+VCwAAALgRLAoYm83Za7Fnj/Tll1LbtlJg4LntDof000/SW285g0ZEhFSzpvM1EyZIa9ZIiYk+Kh4AAABXrABfF4CsBQU551107iydOSMtXy7973/Om+jt3u25765dzuXzz53P/fykq6+W6taV6tSRrrtOuvZaqWxZZ3ABAAAA8hrBohAoVsw5kbt9e+fz48elH390LqtXS7/+6uzJcElPl377zblMnXpufalS0jXXOEOG62f16lJkpDOMAAAAAJeLYFEIlSnjHAbVoYPzeVKStGWLtGGDM2T8+qu0bZtn2JCkf/5xBpHVqz3X2+3O+2hUrXpuqVbN+TMqSgoJ8canAgAAQGFGsLCAoCDp5pudi0tysrR1q7Rpk7R9+7kejEOHMr8+OVnaudO5ZKVUKWfAiIpy9m64HkdFSRUqOIdYhYYyzAoAAOBKRrCwKLtduukm55LRqVPSjh3OkLF9u/THH+eWpKSsj/XPP85l8+aLv1/ZspmXiAjnzzJlnAGlZEnnz+LFCSIAAABWQrC4wpQoIdWv71wySk+XDh8+FzL27JH27XNe6vbAAWdPR2rqhY+bnCz99ZdzyQl//3MhI2PgKFXKWWPx4s4lNPTCj4ODCScAAAAFBcECkpyTtytWdC6NGmXenpYmHTt2Lmi4liNHpKNHzy1xcZIx2b9fWppz37i43NXsChnFijnnggQHX9pP1+OgIOd9ROz2i/8MCCDMAAAAZIVggRzx95fKl3cuGedynC811RkWXEHj2DHnzxMnnMOpTp48N7TK9fz06curKT3d+drLff3lsNk8g0ZW4cMVQC62+Pn56/DhWlq40C9H+5+/+Ps7g5Wfn+djbz+32c4t5z/P7QIAAAqXQhMsjDEaMWKEPvroI50+fVotW7bUpEmTVKZMGV+XhgwCAqRy5ZxLTqWmOud+nDzpDCDx8c4lIcG55OTxmTPOGwOmpeXbR5Pk7I1JTnYuueMnKToPKrK2vAwqlxpozg83F9qWm8dOAfr332YqWjTA47LPefke+VF7fr2Ht/nqvbN6X2P89c8/DfTWW/75VhffdeF5X2P8deLEbRo//tLbQ2H9zIXtfb3FGH9FR1dR27a+riR7hSZYvPnmm3r33Xf12WefqXTp0nr88cfVrVs3LVq0yNelIZcCAqTwcOdSvXrujuVwSGfPOkNGYuK5x+f/PP9xcrKUkpL9z+z2SU7O2VAw5IwxV8L3aZNUzNdFoEDwkxTu6yJQYPhJ4o+nkCQ/tWhR3NdF5EihCBbp6el68803NXjwYLX//7vEvf3222rTpo327dunmJgYH1eIgiIw0LmEhvquhvR0Zy/MxZazZx1avnyV6te/XTZbYLb7Z1wcDud7pKc7e2hcj7393PXYdfJvhcXl/DBzoW25eXzuuZHD4VBAQKCcISM/3sMbnyPrbQCAK0ehCBZbt25VXFyc2rRp417XuHFj+fn56eeffyZYoEDx8zs31+JCHA5pz54E3XCDMwjhyuVwpGrRosVq27atAi3cGHIaUrzJV+99ofd1OBxavHix2rRpky9tge+6cL2vw+HQkiVL1Lp160tqD4X5Mxem9/Umh8OhZcu2Sqro61KyVSiCxd69eyXJI0AEBwerTJkyOnjwYJavSU5OVnKGgfDx8fGSnL8cx/m3pPYS1/v66v1RcNAW4EJbwDkOBQQYSfnTFq7E+RWFmTEO2e3pCghwKKBQnK0hv/j5OVSkSLrPz19zolA01TNnzsjPz092u91jfUhIiEd4yGj06NEaPnx4pvVLly5VSEhIvtSZU7GxsT59fxQctAW40BbgQltARrQHuPiqLSQmJuZ430IRLOx2u9LT05WamqqADLE9KSnpgiFh4MCB6t+/v/t5fHy8oqKi1LJlS4X6aAC+w+FQbGysWrRoYekhD8gebQEutAW40BaQEe0BLr5uC65RPzlRKIJFxYrOMWUHDx5U5cqVJTmHOh0/flxVqlTJ8jV2uz1TD4ckBQYG+vwfaEGoAQUDbQEutAW40BaQEe0BLr5qC5fynn7Z7+J7derUUXBwsEcX0IoVK2Sz2dQoq9tEAwAAAPCqQtFjERwcrF69emnIkCGqVKmSihUrpr59+6pnz54qVaqUr8sDAAAArniFIlhI0uuvv66zZ8+qc+fO8vf310MPPaQ333zT12UBAAAAUCEKFna7Xe+//77ef/99X5cCAAAA4DyFYo4FAAAAgIKNYAEAAAAg1wgWAAAAAHKNYAEAAAAg1wgWAAAAAHKNYAEAAAAg1wgWAAAAAHKt0NzHIreMMZKk+Ph4n9XgcDiUmJio+Ph4BQYG+qwO+B5tAS60BbjQFpAR7QEuvm4LrnNn17n0xVwxwSIhIUGSFBUV5eNKAAAAgMIlISFBYWFhF93HZnISPywgPT1df//9t4oXLy6bzeaTGuLj4xUVFaUDBw4oNDTUJzWgYKAtwIW2ABfaAjKiPcDF123BGKOEhARVqFBBfn4Xn0VxxfRY+Pn5KTIy0tdlSJJCQ0P5jwQk0RZwDm0BLrQFZER7gIsv20J2PRUuTN4GAAAAkGsECwAAAAC5RrDwIrvdrqFDh8put/u6FPgYbQEutAW40BaQEe0BLoWpLVwxk7cBAAAA5B96LAAAAADkGsECAAAAQK4RLAAAAADkGsHCC4wxGj58uCpUqKCiRYuqY8eOOn78uK/LQj7YsmWLWrZsqZCQEJUrV06PPvqoTpw44d7+wQcfKCYmRsHBwbrjjju0d+9ej9fPmTNHV199tYKCglSvXj39+uuv3v4IyAdTp06VzWbT9OnT3etoC1ee48ePq3v37ipdurSCg4PVoUMH9zbaw5UjISFBTzzxhEqVKqXixYurc+fOOnz4sHs7bcH6Nm/erDp16mj16tUe63P7u1+5cqXq1q2roKAgXXvttfrf//6X758lE4N898Ybb5hSpUqZ+fPnmx9//NFcffXVpk2bNr4uC/ng9ttvN6NGjTKbN282CxcuNDExMaZt27bGGGNmz55t7Ha7mTp1qlm/fr1p2LChufbaa01aWpoxxpg1a9aYgIAAM27cOLNp0ybTqVMnExERYeLj4335kZBLZ8+eNdHR0UaSmTZtmjGGtnAlio+PNzVr1jQtW7Y0K1asMBs3bjSzZ882xtAerjTdunUzNWrUMN9995358ccfTb169Uzjxo2NMbQFq/v111/NfffdZ4KDg40ks2rVKve23P7u9+7da4oWLWpefPFFs2XLFtOrVy8THBxs9u3b59XPSLDIZ2lpaSY8PNy8/fbb7nWLFy82kszevXt9WBnyw19//eXxfMaMGcbPz8/8+++/pnbt2qZPnz7ubTt27DCSzPfff2+MMaZjx47mrrvucm8/efKksdvt5tNPP/VO8cgXgwYNMvfee69HsKAtXHkGDRpkatSoYZKTkzNtoz1cWa655hrz7rvvup/PmzfPhISEGGNoC1b3yiuvmIceesh89913mYJFbn/3/fr1MzfeeKN7u8PhMBUrVjRDhgzJ50/liaFQ+Wzr1q2Ki4tTmzZt3OsaN24sPz8//fzzzz6sDPkhKirK43lQUJDS09N16tQpbdy40aMd1KxZU+XLl3e3g+XLl3tsL1GihOrUqUM7KcS2bNmiDz74QOPGjXOvoy1cmT777DP16dNHRYoU8VhPe7jydOnSRV9++aWOHj2qU6dO6dNPP1WXLl1oC1eAkSNHatq0aapSpYrH+rz43S9fvlytW7d2bw8ICFCjRo283jYIFvnMNT4uJibGvS44OFhlypTRwYMHfVUWvMAYo08++US33HKLjh49KsmzHUhSpUqVdPDgQZ08eVKnTp264HYUPklJSXrwwQc1ePBgRUZGutfv27dPEm3hSvLXX3/p77//VmhoqJo0aaLSpUvr9ttv1/r162kPV6BBgwbJz89P5cqVU6lSpbR792698847tIUrgM1my3J9Xvzu9+7dWyDaBsEin505c0Z+fn6Z7pYYEhKi5ORkH1WF/OZwOPTkk09q+fLlmjhxos6cOSPJ+XvPyNUOstuOwqdfv34KDw/Xc88957GetnDlcU3Mfeutt/TMM89o4cKFKlGihFq1aqX4+HhJtIcryZNPPqljx45p8eLF+u6771S0aFF16dKF/zZcwfLid3/mzJkC0TYCvPpuVyC73a709HSlpqYqIODc152UlJSpAcAaDh48qC5dumjv3r36/vvvddNNN2ndunWSpJSUFI99Xe3AFTwvtB2Fy+TJkzV37lxt2rRJfn6ef7/J7ndNW7Ce1NRUSdLzzz+v++67T5LzSmERERFasWKFJNrDlWL79u2aMmWK1q1bp3r16kmS5s6dq+joaDVp0kQSbeFKlBf/X7Db7QWibdBjkc8qVqwoSR5dUcnJyTp+/HimMXYo/Hbv3q1bbrlFxYsX1+bNm3XrrbdKOtcODhw44LH/gQMHVKVKFYWHh8tut19wOwqXUaNG6cSJE4qJiVFQUJCCgoIkSY899pgefPBBSbSFK0lERIQkqVq1au51JUuWVEREhIwxkmgPV4qtW7dKkmrVquVeFxUVpfDwcDkcDkm0hStRXpwjVKxYsUC0DYJFPqtTp46Cg4MVGxvrXrdixQrZbDY1atTIh5UhP3Tt2lX169fXokWL3CcTkvMffOXKlT3awe7du3Xw4EE1a9ZMfn5+ql+/vsf206dPa/369WrWrJlXPwNyb9myZdq2bZs2bdrkXiRn4FiyZAlt4QpTtWpVRUREeEyijIuL07Fjx1SrVi3awxXEdQK5fft297rDhw8rLi5O1apVoy1cofLiHKFhw4Ye29PS0vTDDz94v2149RpUV6j+/fubcuXKmSVLlpjVq1ebmjVrmmeffdbXZSGP7dq1y0gyX331lfn99989llOnTpl3333XFC1a1MyePdv88ssvpmHDhqZdu3bu18+fP9/4+/ubDz/80GzatMl07NjR3HjjjSY1NdWHnwp5RRkuN0tbuPKMGTPGlChRwsyaNcusXbvWtGjRwlxzzTUmJSWF9nAFSU9PN3Xq1DG1atUy33//vVm9erVp0KCBiY6ONmfOnKEtXCH27duX6XKzuf3db9iwwQQEBJjhw4ebrVu3ml69epkKFSp4/R4nBAsvSEpKMr169TKhoaGmZMmSpnfv3iYpKcnXZSGPrVixwkjKcpkwYYJJT083r776qgkPDzfFihUzDz74oDl58qTHMSZOnGgqVKhggoODzZ133mkOHDjgmw+DPJcxWNAWrjzp6elmyJAhJiIiwgQFBZk2bdq472VEe7iyHD161HTt2tWUKFHCFCtWzLRv39788ccfxhjawpUiq2CRF7/7r776ylStWtXY7XZz++23m23btnnj43iwGfP/AzwBAAAA4DIxxwIAAABArhEsAAAAAOQawQIAAABArhEsAAAAAOQawQIAAABArhEsAAAAAOQawQIAAABArhEsAAAAAOQawQIAcMVITk5WSkqKr8sAAEsiWAAAtG/fPv3www8e69LS0vTXX39Jkk6fPq3mzZvrzz//vOhxJkyYoG7durmfG2NUvXp1ffnll5KkLVu2KDk5Ocd1/fvvv2rZsqU2b96c7b7fffedUlNTJUm1atXS1KlTJUkrV67U3r17JUmff/65YmJicvz+AICcI1gAAPTRRx+pQ4cO7hNwSfrpp58UHR2tgwcPKjk5Wd99953+/fffbI9TrFgx93ObzaY///xTJ0+eVHp6urp27aqmTZvq6NGjHq+bMGGCFi5cmOl4S5cu1ffff6/y5ctf9H0dDod69+6t559/XpKUmpqq9PR07du3Tx06dNCCBQskSWvXrlXTpk0v/mUAAC4LwQIAoOHDhysqKkpdu3Z1/9V/wYIFql27tiIjI2WMkeQMCheyatUqbd++Xb179/ZYHxISIofDIT8/Py1ZskSnTp1SvXr1tGHDBvc+f/31l+677z59//33Hq+dNm2amjVrpoiIiIvWHxgYqBkzZuibb77RsWPH3OtfeeUVdezYUX379pUxRkuWLFGLFi1y9qUAAC4JwQIAILvdrk8//VS//vqrli1bpvT0dM2dO1cbN26UzWZTuXLlJEnXXHONbDabe5k8ebL7GGPGjFHLli1Vs2ZNj2MXL15c8fHxkqTIyEitWrVKNWrU8JjrMHbsWHXq1EkdO3bU1q1bJUl///23Fi5cqKVLl3q8Z8alcuXKkqTNmzfrjz/+0JgxY7Ry5UrFx8dr/fr1atmypZo1a6bt27dr1apV+vvvv9WjRw8FBAR4LGvXrs3PrxcArggBvi4AAFAw1KtXT7t27VKVKlU0Z84cHThwQOvXr1dYWJgOHz6sRo0a6fvvv1dUVJT7Na6ehHXr1mnRokUaOnRopuOWKlVKJ0+elCQlJCTo2LFjeumll7R9+3adPn1arVq1coeUBg0a6PXXX9esWbP09ttvq3z58lqyZIlSU1N1+vRphYeHu4/7+OOPu4ddrVmzRnPmzJEkHT58WAcOHNDy5cu1c+dOSdIjjzyiefPmqWHDhpo2bZokae/evWrWrJlWrFihWrVq5f0XCgBXGJtx9W8DAK5IZ8+edU+oDgoKUlBQkNq1a6fy5cvr448/luQ8Ca9atar+/PNPVapUKdMxGjRooDVr1mjo0KG655579NNPP+ngwYM6ePCg5s2b5x5e5eq5KF68uCIjI/XAAw/o1VdfdR/n8OHDKlmypOLi4nTVVVdp/PjxeuKJJzRnzhx16dLFfZzff/9dNWvW1IIFC9S2bVv363/88Ufde++9OnXqlG699Vb17NlT999/v3799VfdfPPNuuWWW7RmzRpJ0g8//KA77rhDiYmJCgoKyodvFgCuLPRYAMAVrnfv3vrkk08kOeckvPbaa5ozZ44SEhLc+7gmbRctWjTT6ydPnqy1a9cqLCxMkrRixQp9+OGHioyMVMWKFRUTE6PTp09r4sSJioyMVGRkpHvf87kmaX/zzTcqW7asunfvLkk6deqUAgMDlZ6eLj8/P40bN05Vq1ZVmzZtJEkpKSl688039dprr+m9997T22+/rcqVK+uZZ57RqlWrdPr0acXExGj//v3u99q/f7/Kli1LqACAPMIcCwC4wr399ts6fPiw6tevL0latmyZgoKCVKZMGfdchhtuuEGSFB4enmmeQ//+/fX8888rMjJSkvTss89q27ZtWrJkiT755BN17dpV8fHxatWqla699toLhgrJecnYcePG6ZlnntEvv/yiwMBASc4ek6SkJPdciB49euijjz5yTyZv06aN3njjDU2dOlWPPfaYJKlx48b6+eeftWbNGj355JNasGCBjh49qiNHjkhyzstgCBQA5B16LADgChcaGqrQ0FAVKVJEknNY0++//+6xz5gxY7RmzRrNnz/fY/3Jkyf15JNPasSIEfr222+zPP61116rY8eO6fDhw9leNva1117T/v379fTTT6t06dLu9b/88oskaeHChapfv77q1q3r8boBAwaoevXqqlatmjp16qTXX39dd911lyRpw4YN7gBSo0YNrVq1Svfdd5/WrFnDFaIAIA/RYwEA8BAcHKxq1aq5l7Jly2rJkiXauXOnJkyYoMjISPe2evXqaeXKlbLb7Rc83k033SQ/Pz/33IYL+fHHH/XDDz9o9OjRHsc7efKkVqxYob59+2ratGlKSkrK9NrbbrtNJUqU0ObNm/XNN9/IGKO4uDjFxcXpxIkT7svl3nbbbZo3b56OHz+u9evXq1WrVpf5LQEAzkewAABcUFpamh5//HEZYzRjxgxNmzZNt956q/tqS5JzIvbFlC5dWrVr19bixYsvut+rr76qunXrqkuXLh7rJ06cqIoVK2rMmDE6c+aM3n333Uyvvfvuu1WmTBnVqlVLxhh16NBBZcqUcS+uSeOPPPKI5syZo7feekvh4eFq0KBBTr8KAEA2CBYAgCydPn1aHTp00Pz58zVz5kw98MAD2rBhgwICAlSvXj198cUXOT7W3XffrTlz5ujs2bPudb/++qtmzpwpSfr222+1fPlyjRkzxuMmfHv27NEbb7yhgQMHKigoSIMGDdLrr7+u3bt3exz/hx9+0I8//qiQkBDt2rVLxhgZYzRixAjVq1fPPa+jcePGio6O1tixY/XUU0/Jz4//DQJAXuG/qACATObPn6+rr75aa9as0bfffqvGjRtLkipXrqzVq1erdevWeuCBBzRlypQcHe/xxx/XmTNn9P7777vXLVmyRC+++KJSUlL0/PPPq0mTJmrevLl7+z///KO7775bderU0eOPPy5Jeu655xQdHa3WrVu7J2G7fPbZZ7Lb7Zo/f74SEhK0cuVKvfHGG3rrrbfc+6Snp7vvw8HEbQDIWwQLAIDmz5+vtWvXas2aNUpJSVFYWJhuvfVWbdq0SXfccYfHvkFBQZo9e7ZGjRrlniCdnfLly6tv374aOnSoNm/eLElau3at6tSpo9jYWO3evVvDhw937793717dfvvtcjgc+uKLL9y9GAEBAZo3b57Onj2rpk2buo8lSZMmTdLcuXO1cOFCRUVF6c4779SLL76oRo0auffp27evli9frhtvvFHdu3fXxo0bL/s7AwB4IlgAwBVu+vTpuueeezRo0CCdOXNGN954o7Zv366XX35ZZ8+e1Z49e/THH3/ojz/+0J49e7R7927t3LlT7du3159//qmjR4/m6H1ee+01XX311WrcuLFeeOEFLVu2TI0bN9add96pX3/9VY0aNVJaWpo+/PBD1a5dW+np6Vq+fLkqVKjgcZzKlStr8eLFOnnypG6++WZNnTrVvc3Pz092u11+fn66+uqrNWrUKPXt21fJycnq2bOn3nvvPX3yySdavXq1qlWrpiZNmrjvxA0AyB3uvA0AV7i3335bR44c0dixY3X27FmNGzdOs2fP1t69e3XmzBll97+JrVu36rrrrtN1112ne++9V8OGDbvgvidPnlTv3r01Z84cXXfddYqNjVWJEiXc2+Pi4lS7dm21b99eb731lkJCQi54rIMHD+qxxx7TRx99pA8//FCzZs1SXFycHnvsMQ0fPlylS5fW119/rUOHDunzzz/Xtm3bNGnSJD388MOSpOPHj6tz58764YcftGrVKjVs2PCSvjcAgCeCBQBc4VJSUhQYGOgxaTqj9PR0paenewQM183x/P393etOnDghu92uYsWK5aqehISEbK80db6PP/5YRYoUUadOnbJ87X/+8x81a9Ys07yKtLQ0zZkzR507d85NyQAAESwAAAAA5AHmWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADINYIFAAAAgFwjWAAAAADItf8DttM/XmcrKbUAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 多元线性回归 梯度下降\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "# 生成模拟数据 模拟出有3个特征 + 一个常数项（总共4维）；\n",
    "np.random.seed(0)\n",
    "m = 100 # 样本数量\n",
    "n = 3 # 特征数量（不含截距）\n",
    "\n",
    "X = np.random.rand(m, n)\n",
    "X = np.c_[np.ones(m), X]  # 截距项 全1列 对应常数项相乘\n",
    "\n",
    "# print(\"X矩阵：\", X)\n",
    "theta_true = np.array([4, 3, -2, 1])\n",
    "y = X @ theta_true + np.random.randn(m) * 0.5\n",
    "\n",
    "# 梯度下降初始化\n",
    "theta_gd = np.zeros(n + 1)  # 初始化参数 θ，全为0\n",
    "alpha = 0.1 # 学习率\n",
    "iterations = 1000\n",
    "\n",
    "cost_history = []\n",
    "# 梯度下降训练\n",
    "for i in range(iterations):\n",
    "    predictions = X @ theta_gd\n",
    "    errors = predictions - y\n",
    "    gradient = (1/m) * X.T @ errors\n",
    "    theta_gd = theta_gd - alpha * gradient\n",
    "\n",
    "    cost = (1/(2*m)) * np.sum(errors ** 2)   # 损失函数 J(θ)\n",
    "    cost_history.append(cost)\n",
    "    if i % 100 == 0:\n",
    "        print(f\"梯度下降迭代{i}: 损失 J(θ) = {cost:.4f}\")\n",
    "\n",
    "print(\"梯度下降求得参数：\", theta_gd)\n",
    "print(\"真实参数 θ_true：\", theta_true)\n",
    "\n",
    "# 正规方程法求解（矩阵满秩可用）\n",
    "theta_ne = np.linalg.inv(X.T @ X) @ X.T @ y\n",
    "print(\"正规方程求得参数：\", theta_ne)\n",
    "\n",
    "# 预测值\n",
    "y_pred_gd = X @ theta_gd\n",
    "y_pred_ne = X @ theta_ne\n",
    "\n",
    "# 画图比较预测值和真实值\n",
    "plt.figure(figsize=(10,5))\n",
    "\n",
    "plt.scatter(range(m), y, color='blue', label='真实值 y')\n",
    "plt.scatter(range(m), y_pred_gd, color='red', alpha=0.6, label='梯度下降预测值')\n",
    "plt.scatter(range(m), y_pred_ne, color='green', alpha=0.6, label='正规方程预测值')\n",
    "\n",
    "plt.xlabel('样本序号')\n",
    "plt.ylabel('目标变量值')\n",
    "plt.title('多元线性回归预测值 vs 真实值')\n",
    "plt.legend()\n",
    "plt.show()\n",
    "\n",
    "# 绘制损失函数图像\n",
    "plt.figure(figsize=(8, 5))\n",
    "plt.plot(range(iterations), cost_history, 'b-', linewidth=2)\n",
    "plt.title(\"损失函数 J(θ) 随迭代次数的变化\", fontsize=14)\n",
    "plt.xlabel(\"迭代次数\", fontsize=12)\n",
    "plt.ylabel(\"损失 J(θ)\", fontsize=12)\n",
    "plt.grid(True)\n",
    "plt.tight_layout()\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1bbdba75-af0b-4cf7-bfc9-091d727abe65",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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